1. Field of the Invention
The present invention relates, in general, to screw compressors which have a pair of rotors and are used for compressing gas to increase the gas pressure and, more particularly, to a rotor profile for such screw compressors, which is designed to minimize the cross-sectional area of a blow-hole while increasing the minimum pressure angle of a rotor machining tool.
2. Description of the Prior Art
In a screw compressor, a pair of rotors, that is, male and female rotors, are set in the actuating space of a compressor housing while engaging with each other and being supported by bearings, such that the two rotors are rotated relative to each other to gradually reduce the volumes of the compression chambers sealed by the rotors and the compressor housing, thus compressing gas inside the chambers. In the screw compressor, the important parts of the teeth of the female rotor are positioned inside the pitch circle thereof, while the important parts of the teeth of the male rotor are positioned outside the pitch circle thereof. Degree of precision and shapes of male and female rotors typically determine performance of screw compressors, for example, displacement and volumetric efficiency. In a detailed description, in terms of the shapes of the rotors, the performance of the screw compressors is typically determined by the length of a seal line and the cross-sectional area of a blow-hole such that the performance is enhanced in accordance with a reduction of both the length of the seal line and the cross-sectional area of the blow-hole. Shapes of rotors for screw compressors have been actively studied in recent years, and many patent applications for the rotor shapes have been filed in many countries. However, in accordance with performance tests for screw compressors having the above-mentioned rotors, small pressure angles of rotor machining tools used in the process of producing the rotors degrade the performance of resulting screw compressors more seriously than long seal lines or large-sized blow-holes. That is, when the rotor machining tools have small pressure angles, the tools may fail to machine precise rotors, so that it is almost impossible to assemble the rotors in the housing of a screw compressor, or the tools may cause large machining errors in the produced rotors due to the portions of the tools having the small pressure angles, thus resulting in an increase in the leakage of gas through the parts of the rotors having the large machining errors and degrading operational efficiency of the screw compressors.
Examples of conventional rotor profiles for screw compressors may be referred to U.S. Pat. No. 4,412,796, UK Patent Nos. 1197432 and 2092676. The rotors disclosed in the above three patents have asymmetric rotor profiles different from conventional symmetric rotor profiles, so that the compressor performance is enhanced. In the rotor profiles disclosed in U.S. Pat. No. 4,412,796 and UK Patent No. 2092676, the addendum of a female rotor is designed to be relatively large in comparison with the outer diameter of the female rotor and the dedendum of a male rotor engaging with the female rotor is designed to be relatively large in comparison with the outer diameter of the male rotor, so that the volume of the actuating space of a compressor housing is preferably increased. However, the above rotor profiles undesirably increase the blow-hole sizes, thus reducing volumetric efficiency and adiabatic efficiency of resulting compressors. Definition of the technical term xe2x80x9cblow-holexe2x80x9d is described as follows with reference to FIGS. 1 and 2. That is, the curve F-G of each female rotor tooth defined at a position around a trailing end of the female rotor tooth is designed to have a constant curvature. Therefore, when the male and female rotors are rotated after the point xe2x80x9cFxe2x80x9d of a female rotor tooth comes into contact with the point xe2x80x9cfxe2x80x9d of a male rotor tooth, the two rotors are not kept in contact with each other, but are separated from each other. At this time, a three-dimensional space is defined between the compressor housing and the two rotors, thus causing leakage of gas from a high-pressure chamber into a low-pressure chamber inside the housing. The above-mentioned three-dimensional space having a triangular cross-section is known as a so-called xe2x80x9cblow-holexe2x80x9d in the technical field. In an effort to minimize the size of the blow-hole, the female rotor profile may be designed to remove the curve F-G from each female rotor tooth, and, at the same time, the male rotor profile may be designed to extend the curve D-E, generated by the male rotor, to an addendum circle of the female rotor, thus completely preventing formation of the blow-hole between the rotors, and the housing. In such a case, the blow-hole size becomes zero, and it is possible to ideally prevent leakage of gas from the high-pressure chamber into the low-pressure chamber. However, unfortunately, it is impossible to practically produce male and female rotors having the above-mentioned rotor profile.
In addition, in terms of workability and production cost regarded as very important factors determining productivity of rotors for screw compressors, the rotor profile disclosed in UK Patent No. 1197432 has a portion with a pressure angle of zero, thus undesirably causing severe frictional wear of rotor machining tools while producing rotors and resulting in difficulty in precise machining of the rotors. The rotor profiles disclosed in UK Patent No. 1197432 and U.S. Pat. No. 4,412,796 result in formation of point-generated portions around the trailing ends of the rotor teeth, so that it is very difficult to machine the rotors and the point-generated portions of the rotor teeth are severely worn due to friction. The point-generated portions of the rotor teeth thus result in severe damage to the rotors, and reduce the expected life span of the screw compressors. Furthermore, the pointed-generated portions of the rotor teeth shorten the expected life span of bearings and filters used in the screw compressors.
In an effort to overcome the above-mentioned problems, Korean patent Laid-open Publication No. 95-27198 proposes a rotor profile for screw compressors. As shown in FIG. 9, the rotor profile disclosed in the above Korean patent, includes both a curve d2xe2x88x92c2 generated by a portion of the male rotor""s tooth profile defined by an optimum quadratic function, f(x)=ax2+bx+c, and a circular arc c2xe2x88x92b2, so that it is possible to desirably reduce a vacuum space in a compressor and converge the slip coefficient at drive parts of rotors to zero. However, the above rotor profile is disadvantageous in that the radius of curvature of a curve a2xe2x88x92b2 generated at a portion around the trailing end of each of the female rotor teeth is excessively reduced to degrade productivity of rotors and fails to improve operational efficiency of a screw compressor, even though the reduced radius of curvature of the curve generated at the trailing end of each female rotor tooth somewhat reduces the size of a blow-hole to enhance the operational efficiency of the screw compressor. That is, the reduced radius of curvature of the curve generated at the trailing end of each female rotor tooth undesirably reduces the pressure angle of a rotor machining tool to 5xc2x0, thus resulting in excessive errors on produced rotors and thereby downgrading productivity of the rotors and failing to improve operational efficiency of screw compressors. In the rotor profile disclosed in the above Korean patent, the curve c2xe2x88x92b2 of the female rotor tooth defining the blow-hole is a circular arc, so that the reduction of the size of the blow-hole is not sufficient. A screw compressor having the above rotor profile is advantageous in that the rotors have a tooth ratio of 4:5 (numbers of male and female rotor teeth: 4+5) capable of preferably reducing the rotor machining time and saving the material of rotors because it is possible to produce the rotors using small-sized materials. However, the rotor profile is problematic in that it excessively reduces the diameter of a drive rotor and does not allow a desired increase in the size of bearings, and often causes the severe problem of an excessive reduction of axial strength of rotors under high-pressure operating conditions.
Accordingly, the present invention has been made keeping in mind the above problems occurring in the prior art, and an object of the present invention is to provide a rotor profile for screw compressors, which determines a curve positioned around the trailing end of each of female rotor teeth by using a hyperbola function capable of increasing the minimum pressure angle of a rotor machining tool, thus minimizing the cross-sectional area of a blow-hole while allowing the rotor machining tool to desirably produce precise rotors under agreeable machining conditions.
Another object of the present invention is to provide a rotor profile for screw compressors, which is designed to optimize the wrap angles of rotors, thus increasing the minimum pressure angle of a rotor machining tool while maintaining desired strengths of the rotors.
A further object of the present invention is to provide a rotor profile for screw compressors, which is designed to use a female rotor as a drive rotor, thus minimizing leakage of gas from a high-pressure chamber into a low-pressure chamber, and which has a tooth ratio of 4:6 (numbers of male and female rotor teeth: 4+6), thus enhancing the axial strength of rotors under high-pressure operating conditions and improving workability during a process of machining rotors, and providing rotors having improved performance.
In order to accomplish the above objects, the present invention provides a rotor profile for screw compressors, which is shown in a latitudinal cross-section taken along a line extending in a direction perpendicular to rotor axes and applied to male and female rotors used in a screw compressor having a housing defining an actuating space therein, the male rotor being rotatably set in the actuating space and having spiral teeth and roots defined between the teeth, and the female rotor being set in the actuating space to rotatably engage with the male rotor and having spiral teeth and roots defined between the teeth, the rotor profile comprising: a first curve F-G determined as a circular arc and inscribed in an addendum circle of the female rotor at a point xe2x80x9cGxe2x80x9d around a trailing end of each tooth of the female rotor; and a second curve determined by a hyperbola function r=(xcex5xc2x7K)/(1xe2x88x92xcex5xc2x7cos xcex8), wherein 1.1xe2x89xa6xcex5xe2x89xa61.15, and a derived function of first order of the hyperbola function of the second curve at a point xe2x80x9cFxe2x80x9d is equal to a derived function of first order of a function of the curve F-G. In the rotor profile, the male rotor has a wrap angle larger than 300xc2x0 and not larger than 310xc2x0.
In the rotor profile, the male rotor has a male rotor profile with curves a-b, b-c, c-d, d-e, e-f, f-g and g-a, and the female rotor has a female rotor profile with curves A-B, B-C, C-D, D-E, E-F, F-G and G-A. In the male rotor profile, the curve a-b is a generated curve which is generated by the curve A-B of the female rotor; the curve b-c is a generated curve which is generated by the curve B-C of the female rotor; the curve c-d is a generated curve which is generated by the curve C-D of the female rotor; the curve d-e is a circular arc which is inscribed in an addendum circle of the male rotor and has a center of curvature on a line extending between centers of the male and female rotors; the curve e-f is a generated curve which is generated by the curve E-F of the female rotor; the curve f-g is a generated curve which is generated by the curve F-G of the female rotor; and the curve g-a is a circular arc which is defined along a dedendum circle of the male rotor and has a center xe2x80x9c0 mxe2x80x9d of curvature at the center of the male rotor. In the female rotor profile, the curve A-B is a circular arc which is inscribed in the addendum circle xe2x80x9cAfxe2x80x9d of the female rotor at a point xe2x80x9cAxe2x80x9d, is circumscribed on the curve B-C at a point xe2x80x9cBxe2x80x9d and has a center xe2x80x9c01xe2x80x9d of curvature; the curve B-C is a circular arc which is circumscribed on the curve A-B at the point xe2x80x9cAxe2x80x9d, is circumscribed on the curve C-D at a point xe2x80x9cCxe2x80x9d, and has a center xe2x80x9c02xe2x80x9d of curvature; the curve C-D is a circular arc which is circumscribed on the curve B-C at the point xe2x80x9cCxe2x80x9d, and is inscribed in the addendum circle xe2x80x9cAmxe2x80x9d of the male rotor at point xe2x80x9cDxe2x80x9d, and has a center xe2x80x9c03xe2x80x9d of curvature on the line extending between the centers of the male and female rotors; the curve D-E is a generated curve which is generated by the curve d-e of the male rotor; the curve E-F is a curve determined by the hyperbola function r=(xcex5xc2x7K)/(1xe2x88x92xcex5xc2x7cos xcex8), wherein 1.1xe2x89xa6xcex5xe2x89xa61.15, xcex8 is a variable, a derived function of first order of the hyperbola function of the curve E-F at a point xe2x80x9cExe2x80x9d is equal to a derived function of first order of a function of the curve D-E, and a derived function of first order of the hyperbola function of the curve E-F at the point xe2x80x9cFxe2x80x9d is equal to the derived function of first order of the function of the curve F-G; the curve F-G is the circular arc which is inscribed in the addendum circle of the female rotor, and the derived function of first order of the function of which at the point F is equal to the derived function of first order of the hyperbola function of the curve E-F; and the curve G-A is a circular arc which is defined along the addendum circle of the female rotor and has a center of curvature at the center xe2x80x9c0fxe2x80x9d of the female rotor.